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Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals
A. V. Ivanov, M. A. Kurkov, D. V. Vassilevich
Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chir…
Atiyah-Patodi-Singer Index Theorem for Domain Walls
A. V. Ivanov, D. V. Vassilevich
We consider the index of a Dirac operator on a compact even dimensional manifold with a domain wall. The latter is defined as a co-dimension one submanifold where the connection ju…
Nearly associative deformation quantization
D. Vassilevich, F. M. C. Oliveira
We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identiti…
Spectral geometry of symplectic spinors
Dmitri Vassilevich
Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by K.~Habermann. Here we study the spectral geometry aspects of the…
Global and local aspects of spectral actions
Bruno Iochum, Cyril Levy, Dmitri Vassilevich
The principal object in noncommutatve geometry is the spectral triple consisting of an algebra A, a Hilbert space H, and a Dirac operator D. Field theories are incorporated in this…
Spectral problems from quantum field theory
Dmitri V. Vassilevich
We describe how spectral functions of differential operators appear in the quantum field theory context. We formulate consistency conditions which should be satisfied by the operat…